Lecture 4 Flashcards
Give three options for visualization of compressible flow features
- Schlieren technique (1st derivative of density)
- Shadowgraphy (2nd derivative of density)
- Mach-Zehnder interferometry
What does a schlieren knife do?
It cuts out the portion of light under a special angle that can be selected by its position. This leads to darker regions in the flow, which correspond to changes in density (decrease) and therefore acceleration of the flow.
Which quantity is visualized in Schlieren and Shadow imaging?
- Schlieren technique (1st derivative of density). Direction can be adjusted by the position of the knife.
- Shadowgraphy (2nd derivative of density)
How can a boundary layer in a nozzle be visualized?
- You would choose for example Schlieren technique
- You would position the knife in normal direction
- You will get the density gradient in normal direction. You can visualize then the boundary layer.
What properties do hyperbolic processes usually have?
- They have some kind of direction
- They have some kind of speed
If the hyperbolic process is hyperbolic in time (order 2 in time), then the speed is a real speed. This is the propagation speed for example
How is the characteristic velocity defined?
Given a function f(y), the “caracteristic velocity” is the partial derivative of f(y) with respect to y.
Besides, the characteristic velocity defines a curve dx/dt. This is the “characteristic curve”, that is dx/dt = df(y)/dy.
y is called the “characteristic quantity”.
How is a characteristic curve defined?
The characteristic velocity defines a curve dx/dt. This is the “characteristic curve”.
Why are characteristic quantities constant along characteristic curves?
Demonstration in the paper. But basically, after making some changes with the hyperbolic curve, we obtain that dy=0. This means, the characteristic quantites do not change throught the characteristic curves.
State the equations of the 3 differents PDE
Put an example of them
Parabolic: time (order 1) + space(order 2)
Elliptic: space (order 2Darker zones: Reduction of density –> Acceleratuion of the flow –> Expansion wave)
Hyperbolic: time (order 2) + space(order 2)
Examples look for them in the slides
What represent lighter and darker zones, when applying schlieren technique?
Darker zones: Reduction of density –> Acceleration of the flow –> Expansion wave
Lighter zones: Increase of density –> Deceleration of the flow –> Compression wave
How can we see if the method applied is schlieren o shadowgraphy?
If we can see a single clear line, it is shadowgraphy. If we see entire white or black zones, it is Schlieren.
What does Mach-Zehnder compute?
It computes changes in density, but via isocores lines. Along these lines, density is constant. Then, with the isentropic relations we can compute the Mach number.
What do parabolic PDE?
What’s an example of it?
They try to reduce gradients, by smoothing conditions.
An example is the viscosity in Navier-Stokes-Equations.
